High-capacity digital image watermarking based on waveform modulation of image components

ABSTRACT

Digital watermark information is inserted into an image by first separating the image into components, e.g., discrete cosine transform (DCT) blocks or image subbands, and then associating one or more bits of the digital watermark information with each of the components. For example, a single bit may be associated with each of the components by modulating the components with selected waveforms representative of the corresponding digital watermark information bits. As another example, the digital watermark information bits may be coded, e.g., using a repetition code, linear block code or convolutional code, to form channel bits, such that the modulating waveforms are selected for the image components based on the corresponding channel bits. The digital watermark information may include a total of B bits of information for representing a particular watermark, such that M=2 B  distinct watermarks can be generated using the B information bits. The invention also provides techniques for determining an upper bound on the number of distinct watermarks that can be reliably detected in a given embodiment, as a function of the noise variance of a potential jammer.

RELATED APPLICATION

The present application claims the benefit of U.S. ProvisionalApplication No. 60/102,782, filed Oct. 2, 1998 and entitled “CapacityIssues in Digital Image Watermarking.”

FIELD OF THE INVENTION

The present invention relates generally to image processing techniques,and more particularly to techniques for processing images to incorporatedigital watermarking information.

BACKGROUND OF THE INVENTION

Digital watermarking techniques are used to protect electronic data fromunauthorized copying or distribution. Unlike a traditional visiblewatermark used on paper, a digital image watermark is generally designedso as not to alter the perceived quality of the electronic content,while also being robust to attacks. For example, in the case of imagedata, typical signal processing operations, such as linear and nonlinearfiltering, cropping, rescaling, noise removal, lossy compression, etc.,should ideally be configured such that if any of these operations resultin alteration or suppression of the inserted watermark, then theresulting image must be so severely degraded to render it worthless.However, it is equally important that the digital watermark not alterthe perceived visual quality of the image. It is therefore clear thatfrom a signal processing viewpoint, the two basic requirements for aneffective watermarking technique, i.e., robustness and transparency,conflict with each other.

Digital watermarking applications can generally be grouped into two maincategories: source-based applications and destination-basedapplications. Digital watermarks in source-based applications aretypically used for purposes of ownership identification and tamperdetection. A unique watermark signal is hidden in all copies of aparticular image, prior to their distribution. Examination of theparticular watermark signal hidden in a given image can then be used todetermine the originator of the image, and whether parts of the imagehave been tampered with, e.g., if the picture in a photo identificationhas had the face replaced, etc. Furthermore, digital watermarks can beused to embed application-dependent information, not necessarily dealingwith security issues, that can be maintained even when the image istransferred across different media such as disk, D1 tape, high-qualityprintouts, etc.

Digital watermarks in destination-based applications are typically usedfor tracing purposes. In such applications, a distinct watermark signalthat uniquely identifies a particular copy of the image is hidden inthat copy, prior to its distribution, and acts as a “serial number” forthe image. Then, in the event that multiple unauthorized copies of agiven image are detected, retrieval of that serial number from one ofthe copies of the image can identify the particular user whose image wasutilized to create the unauthorized copies.

It is known that spread-spectrum communication techniques, as describedin, e.g., R. Blahut, “Digital Transmission of Information,” AddisonWesley Publishing Company, 1990, can also be applied to increase therobustness of digital watermarks. In spread-spectrum communicationsystems, an information-bearing narrowband signal is converted into awideband signal prior to transmission, by modulating the informationwaveform with a wideband noise-like waveform that is unknown to ajammer. As a result of this bandwidth expansion, within any narrowspectral band, the total amount of energy from the information signal issmall. However, by appropriately combining all these weak narrowbandsignals at the demodulator, the original information signal isrecovered. Hence a jammer, unaware of the shape of the wideband carrier,is forced to spread its available power over a much larger bandwidth,thus reducing its effectiveness.

The application of the above-described spread-spectrum communicationtechniques to digital watermarking is described in, e.g., I. Cox, J.Killian, T. Leighton, and T. Shamoon, “Secure Spread SpectrumWatermarking for Multimedia,” Technical Report 95-10, NEC ResearchInstitute, 1995. In this approach, robustness and transparency areensured by introducing many small changes into the mostperceptually-significant image components. Since during the watermarkextraction process the location and value of these changes are known, itis possible to concentrate the information of all the small changes tocome up with a robust decision on the presence or absence of aparticular digital watermark. Furthermore, in order to destroy such awatermark, a substantial amount of noise would be required in all theperceptually-significant components, thereby drastically reducing theperceived image quality.

These and other conventional digital watermarking techniques may makeuse of models of the human visual system. Recently, visual models havebeen developed specifically for the performance evaluation of lossyimage compression algorithms, e.g., A. Watson, G. Yang, J. Solomon, andJ. Villasenor, “Visibility of Wavelet Quantization Noise,” IEEETransactions on Image Processing, 6(8), pp.1164-1175, August 1997. Onecommon paradigm for perceptual image coding is based on deriving animage dependent mask containing a set of just noticeable difference(JND) thresholds used to compute perceptually-based quantizers. Thesemodels, originally designed for perceptual coding applications, are alsowell suited for watermarking. For example, the JND thresholds can beused as upper bounds on watermark intensity levels. Hence, a criterionis available to address simultaneously the conflicting goals ofrobustness and transparency: a watermark can be made maximally strong,subject to an invisibility constraint determined from the JNDthresholds. An effective watermarking technique based on theseprinciples is described in C. Podilchuk and W. Zeng, “Image AdaptiveWatermarking Using Visual Models,” IEEE Journal on Selected Areas inCommunications, 16(4), May 1998.

Other conventional digital image watermarking techniques are describedin, e.g., J. O. Ruanaidh, W. Dowling, and F. Boland, “WatermarkingDigital Images for Copyright Protection,” IEEE Proceedings on Vision,Image and Signal Processing, 143(4), pp. 250-256, August 1996, and J.Smith and B. Comiskey, “Modulation and Information Hiding in Images,”Lecture Notes in Computer Science (1174), Springer-Verlag, August 1996.A significant problem with these and other conventional techniques isthat they fail to address adequately the issue of how many watermarkscan be reliably encoded. For example, because the approach in the J.Smith and B. Comiskey reference fails to differentiate between imagedata and impairments introduced by a jammer, the number of differentwatermarks that can be reliably distinguished is significantly reduced.

SUMMARY OF THE INVENTION

In accordance with the invention, digital watermark information isinserted into an image by first separating the image into components,e.g., discrete cosine transform (DCT) blocks or image subbands, and thenassociating one or more bits of the digital watermark information witheach of the components. In an illustrative embodiment of the invention,a single bit of digital watermark information is associated with each ofthe components by modulating the components with selected waveformsrepresentative of the corresponding digital watermark information bits.For example, the selected waveforms may comprise a pair of n-bit vectorshaving a zero mean and an identity covariance matrix, with one of thevectors representing a binary one, and the other representing a binaryzero. The digital watermark information may include a total of B bits ofinformation for representing a particular watermark, such that M=2^(B)distinct watermarks can be generated using the B information bits. Avisual model may be used to determine a particular subset of the imagecomponents to be associated with one or more bits of the digitalwatermark information, so as to ensure that modification or deletion ofthe watermark information will render the resulting image unusable.

In another possible embodiment of the invention, the digital watermarkinformation bits may be coded, e.g., using a repetition code, linearblock code or convolutional code, to form channel bits, such that themodulating waveforms are then selected for the image components based onthe corresponding channel bits. For example, B digital watermarkinformation bits to be inserted in a given image may first be mapped toN channel bits using an (M, N) code, where M=2^(B) is the number ofdistinct watermarks, and N is the block length of the code and thenumber of image components. A given one of the N channel bits is thenassociated with a corresponding one of the N image components bymodulating that component with an appropriately-selected modulationwaveform.

Advantageously, the invention provides practical techniques forinserting and detecting a large number of distinct watermarks, in asimple and cost-effective manner, and without the problems associatedwith the above-described conventional techniques. For example, anembodiment in which B=32 watermark information bits are stored in 8×8pixel DCT blocks of a 512×512 pixel image can reliably distinguish onthe order of 2³²≈4·10⁹ distinct watermarks, which is sufficient for manyhigh-capacity digital watermarking applications. Further increases incapacity can be achieved by increasing the number of watermark bitsstored in the image components. The invention can also be used todetermine an upper bound on the number of distinct watermarks that canbe reliably detected in a given embodiment, as a function of jammernoise variance. These and other features and advantages of the presentinvention will become more apparent from the accompanying drawings andthe following detailed description.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 illustrates the manner in which an image can be modeled as anarray of storage devices in accordance with the techniques of theinvention.

FIG. 2 shows a model of a discrete time channel with additive noise,which comprises an element of the array of FIG. 1.

FIG. 3 is a block diagram showing an illustrative embodiment of anencoder in accordance with the invention.

FIG. 4 is a block diagram showing an illustrative embodiment of adecoder in accordance with the invention.

FIGS. 5 and 6 are plots showing performance data based on a numericalsimulation of a digital image watermarking technique in accordance withthe invention.

DETAILED DESCRIPTION OF THE INVENTION

The present invention will be illustrated in the context of an exemplarydestination-based digital image watermarking application, in which eachwatermark serves as a unique embedded identifier or “serial number” forthe image in which it is embedded. It should be understood, however,that the techniques of the invention are more generally applicable toany digital watermarking application in which it is desirable to improvewatermark reliability, including source-based digital imagewatermarking, and digital watermarking of video or other types ofelectronic data. The term “image” as used herein is therefore intendedto include electronic data such as a video frame or set of frames.

In a destination-based digital image watermarking application, an attackthat does not eliminate a given watermark completely is still successfulif it changes the watermark to the point that a different identifier isrecovered when the watermark is read. It is therefore important todetermine the maximum number of different watermarks that can bedistinguished reliably, and to provide suitable watermarking techniquesto approximate that maximum. These objectives are achieved in anillustrative embodiment of the invention in which it is assumed thatattacks on the watermarks can be modeled as additive noise. As will bedescribed below in conjunction with FIGS. 1 and 2, it can be shown thatthe process of inserting a watermark may be analogized to that ofstoring bits in certain devices, such that the storage capacity of thesedevices provides an indication of the maximum number of watermarks thatcan be distinguished reliably. A simple encoder and decoder architecturefor inserting watermarks so as to approximate the maximum will bedescribed below in conjunction with FIGS. 3 and 4.

Techniques for modeling images as storage devices for watermarkingpurposes, and for computing the storage capacity of such devices, willnow be described in greater detail. In C. Podilchuk and W. Zeng, “ImageAdaptive Watermarking Using Visual Models,” IEEE Journal on SelectedAreas in Communications, 16(4), May 1998, a technique for insertingwatermarks is described, in which an image is broken into N components

C ^((k)) =[c ₁ ^((k)) , . . . , c _(n) ^((k)) ], k=1 . . . N.

These components can be, e.g., blocks of DCT coefficients or sets ofsubband coefficients. For each component, define a vector

P ^((k)) =[p ₁ ^((k)) , . . . , p _(n) ^((k)) ], k=1 . . . N

of positive real numbers, where each p_(i) ^((k)) denotes the maximumstandard deviation of the noise that can be tolerated by c_(i) ^((k))yet still remains perceptually invisible. The vectors P^((k)) arecomputed based on models of the human visual system, which as previouslymentioned have been developed in the context of perceptual coding. Awatermark is inserted in an image by generating random vectors

 W ^((k)) =[w ₁ ^((k)) , . . . , w _(n) ^((k)) ], k=1 . . . N

with a mean of zero and an identity covariance matrix I. The watermarkedimage is then defined to be an image having components

M ^((k)) =[c ₁ ^((k)) +p ₁ ^((k)) w ₁ ^((k)) , . . . , c _(n) ^((k)) +p_(n) ^((k)) w _(n) ^((k)) ], k=1 . . . N.

Given an arbitrary set of image components {tilde over (C)}^((k)), awatermark is retrieved simply by inverting the operations definingM^((k)):${{\hat{W}}^{(k)} = \left\lbrack {\frac{{\overset{\sim}{c}}_{1}^{(k)} - c_{1}^{(k)}}{p_{1}^{(k)}},\ldots,\frac{{\overset{\sim}{c}}_{n}^{(k)} - c_{n}^{(k)}}{p_{n}^{(k)}}} \right\rbrack},{k = {1\quad \ldots \quad N}}$

In accordance with the invention, an image can be considered asrepresenting an array of storage devices by viewing the C^((k)) imagecomponents as “boxes” in which the random vectors W^((k)) are stored.

Consider now the process of retrieving a watermark. In general, eitherdue to intentional attacks or due to normal image processing operations,W^((k)≠Ŵ) ^((k)). The above-noted storage devices are therefore regardedas being “imperfect.” In accordance with the invention, theseimperfections can be modeled as additive noise. That is,

Ŵ ^((k)) =W ^((k)) +J ^((k)) , k=1 . . . N

where J^((k))=[j₁ ^((k)) . . . j_(n) ^((k))] is a zero mean randomvector with covariance matrix σI. It should be noted that this additivenoise assumption, although utilized in the description of theillustrative embodiment, is not a requirement of the invention, and neednot be applicable in a given embodiment of the invention.

FIG. 1 shows a diagram of the above-described storage device model, inwhich an image is characterized as an array 10 of N parallel storagedevices 12-1, 12-2, . . . 12-N, with each of the N storage devicesrepresentative of a corresponding one of the C^((k)) image components.Each of the storage devices 12-N is made up of n elements, with each ofthe n elements having a structure corresponding generally to asingle-letter additive noise channel as shown in FIG. 2. A single-letterchannel refers to a channel which receives a single information signal,in this case a digital image watermark information signal w_(i).

The storage capacity of the array 10 of FIG. 1 will now be determined,in order to provide an indication as to the number of watermarks thatcan be reliably stored in such an array. For example, the capacity ofthe array 10 can be determined as a function of the noise variance σ² asfollows. In the single-letter channel of FIG. 2, both watermark signaltransmitter and watermark signal jammer are assumed to have zero mean,i.e., E(W)=E(J)=0, with the transmitter power constrained byE(W²)=P_(T), and the jammer power constrained by E(J²)=P_(J).Furthermore, it is assumed that W and J are independent. Hence, thechannel capacity is given by the mutual information expression I(W;W+J), and of course is a function of the distributions of W and J. Thismutual information expression is described in greater detail in, e.g.,T. Cover and J. Thomas, “Elements of Information Theory,” John Wiley andSons, 1991.

Given this setup, jamming may be defined as a game in which thewatermark signal jammer player chooses a distribution on J to minimizeI(W; W+J), while the watermark signal transmitter player chooses adistribution on W to maximize I(W; W+J). For a game so defined, andletting W*˜N(0, P_(T)), and J*˜N(0, P_(J)), where N (x, y) denotes anormal distribution with mean x and variance y, it is possible to showthat W* and J* satisfy the following saddlepoint conditions

 I(W; W+J*)≦I(W*; W*+J*)≦I(W*; W*+J)

and therefore that${\min\limits_{J}\quad {\max\limits_{W}\quad {I\left( {W;{W + J}} \right)}}} = {{\max\limits_{W}\quad {\min\limits_{J}\quad {I\left( {W;{W + J}} \right)}}} = {\frac{1}{2}{{\log \left( {1 + \frac{P_{T}}{P_{J}}} \right)}.}}}$

The jamming game therefore has a value, i.e., the right-hand side of theabove equation is the capacity of a power-constrained Gaussian channel.In particular, it follows that a deviation from normality for eitherplayer worsens the mutual information from that player's point of view,thus establishing what the optimal transmitter and jammer should be.Based on this single-letter game formulation, the following points canbe made:

1. Mutual information is the appropriate cost function to bemaximized/minimized by the transmitter/jammer of the watermark signal.In other words, the objective is to compute the capacity of a certainchannel, and channel capacity is defined in terms of the above-notedmutual information expression.

2. Playing the above-described jamming game independently on eachsingle-letter channel in the array 10 of FIG. 1 is optimal: anycorrelations existing among different w_(i) ^((k)) or among differentj_(i) ^((k)) could be exploited by the other player in order to increaseor decrease mutual information to his advantage.

3. From the saddlepoint conditions, it follows that W^((k)) should beN({right arrow over (0)}, I), and J^((k)) should be N({right arrow over(0)}, σ²I).

It should be noted that, in many applications, Gaussian distributionsare used as an idealization of some unknown distribution, and deviationsfrom the Gaussian assumption typically result in a degradation of theperformance of an algorithm designed for the Gaussian case. A typicalexample is the approximation of a Minimum Mean-Square Error (MMSE)estimator by its linear version, i.e., in the Gaussian case theestimator and its approximated linear version coincide. However, in thecase of digital image watermarking, assuming that the noise introducedby the jammer of the watermark signal is Gaussian is a worst-case,conservative assumption, i.e., deviations from Gaussian will only helpimprove watermark detection. This is because Gaussian noise is the mostdifficult type of noise to penetrate.

In accordance with the foregoing description, the capacity of the array10 of FIG. 1 as a function of the noise variance σ² is given by:${C(\sigma)} = {{\sum\limits_{k = 1}^{N}\quad {\sum\limits_{i = 1}^{n}\quad {\frac{1}{2}{\log \left( {1 + \frac{1}{\sigma^{2}}} \right)}}}} = {\frac{nN}{2}{{\log \left( {1 + \frac{1}{\sigma^{2}}} \right)}.}}}$

This capacity measure establishes an upper bound on the number of bitsthat can be stored in the array 10.

The invention also provides suitable encoding devices for storing bitsin an image characterized as an array of storage devices as illustratedin FIG. 1. A problem associated with the design of such encoding devicesis the following uncertainty: at the time the watermark is embedded inthe image, there is generally no knowledge available regarding the typeand amount of noise that will be introduced in an attack, but thestorage capacity of the array is a function of the noise variance.

Suppose the goal is to reliably distinguish M=2^(B) differentwatermarks, which will require that B digital watermark information bitsbe stored in the array 10. Furthermore, assume that each of the Ncomponents of the array 10 has a fixed but unknown capacity which is afunction of the noise variance. The above-noted uncertainty can beaddressed by a conservative approach in which only one bit is stored ineach of the N storage devices of the array 10, i.e., in each of N imagecomponents. A determination is then made as to how the probability ofdecoding error is affected as σ² changes.

This approach can be used to design watermarking systems in which theamount of noise that needs to be introduced to bring the probability ofwatermark decoding error to unacceptable levels is also sufficient todegrade the image to the point that it becomes completely worthless.Furthermore, since N>>B in many applications, a given design can be madeeven more robust to attack by mapping the B information bits to Nchannel bits using an (M, N) code, where M=2^(B) is the number ofdistinct watermarks, and N is the block length of the code. Examples ofsuch codes can be found in the above-cited T. Cover and J. Thomasreference. Other codes suitable for use with the invention includerepetition codes, linear block codes and convolutional codes.

FIG. 3 shows an encoder 30 configured in accordance with the invention,for implementing the above-described digital watermarking process. Theencoder 30 includes a discrete cosine transform (DCT) element 32 forgenerating, e.g., 8×8 pixel DCT blocks from an original unwatermarkedimage. A watermark insertion element 34 stores a bit of digitalwatermark information in each of at least a subset of the 8×8 pixel DCTblocks of the image. For example, if the original input image is 512×512pixels in size, a total of 4096 8×8 DCT blocks are generated. Each ofthe 8×8 DCT blocks represents a component of the image in which a bit ofdigital image watermarking information can be stored. The watermarkinsertion element 34 operates in accordance with information suppliedfrom a visual model 35 to determine which of the 8×8 DCT blocks shouldbe used to store the digital watermark information, e.g., which blocksare perceptually most important to the image such that modification ordeletion of the watermark renders the image unusable. As previouslynoted, the digital watermark information in this example is inserted inthe form of a single bit for each of the designated components. Thevisual model 35 may also be used to determine, e.g., the manner in whichthe modulation waveform is applied to a given one of the imagecomponents. For example, the visual model 35 may be used to provide anindication as to how “strongly” a modulation waveform should be appliedto a given component.

As mentioned above, the digital watermark information bits may be mappedto channel bits for storage in each of the components of the image usingan appropriate code. For example, B bits of digital watermarkinformation can be mapped to N=4096 channel bits, such that a singlechannel bit is stored in each of the N=4096 components of the image.

The operation of the visual model 35 may be in accordance withwell-known conventional techniques, such as those described in Andrew B.Watson, “DCT Quantization Matrices Visually Optimized for IndividualImages,” Human Vision, Visual Processing, and Digital Display IV,Bernice E. Rogawitz, Editor, Proc. SPIE 1913-14, 1993.

An example of a pair of suitable channel modulation waveforms for use inthe encoder 30 for storing a single bit in a given image component isthe pair of Gaussian vectors s^((k),b)=[s₁ ^((k),b) . . . s_(n)^((k),b)], where s^((k),b)˜N(0, I) and b=0, 1. In this case, a given bitb=0,1 of digital watermark information is stored in the given imagecomponent by modulating W^((k))=s^((k),b) onto that component ininsertion element 34. The output of the encoding process is awatermarked image 37 which includes a plurality of image components, atleast a subset of which each store a single bit of digital watermarkinformation. For example, component 38 stores a single bit b=0,1 of thedigital watermark of the watermarked image 37, in the form of acorresponding one of the Gaussian vectors s^((k),b).

In the above example, a particular modulation waveform represents alogic “1”, while another modulation waveform represents a logic “0”. Inother embodiments, a single modulation waveform could be used, with alogic “1” being indicated by the presence of the waveform and a logic“0” being indicated by the absence of the waveform. As another example,a logic “1” could be indicated by a positive value of the singlewaveform, and a logic “0” by a negative value of the waveform. These andother types of modulation processes suitable for use with the presentinvention may be implemented in a straightforward manner usingwell-known conventional techniques, as will be apparent to those ofordinary skill in the art.

A more detailed example of the modulation of digital watermarkinformation onto a given image component is as follows. Assume thatthere are N image components, each corresponding to an 8×8 block ofpixels, and that k=1, 2, . . . N. Also assume that there are a total ofB=N bits of digital watermark information to be inserted into the image,i.e., a single bit of digital image watermarking information is to beinserted in each 8×8 component. A given bit of digital imagewatermarking information is represented in this case by a waveformcorresponding to a random vector of length n=8×8=64, i.e., the vectorincludes one element for each pixel of the 8×8 block. More specifically,logic “0” and “1” values are represented as follows:

 0=w ⁽⁰⁾ ={w ₁ ⁽⁰⁾ , w ₂ ⁽⁰⁾ , . . . w _(n) ⁽⁰⁾},

1=w ⁽¹⁾ ={w ₁ ⁽¹⁾ , w ₂ ⁽¹⁾ , . . . w _(n) ⁽¹⁾},

Either a “0” bit or a “1” bit of digital watermark information is addedto a given one of the N components of the image by applying thecorresponding length-n random vector to the n elements of thatcomponent. Perceptual weights generated by the above-noted perceptualmodel may be used to determine how strong each element of the randomvectors can be without significantly degrading image quality. Theresulting element of a given one of the N watermarked image componentsis given by:

m _(i) ^((k)) =c _(i) ^((k)) +p _(i) ^((k)) w _(i) ^((j)),

where i=1, 2, . . . n, j=0, 1, and k=1, 2, . . . N. The givenwatermarked component is given by:

M ^((k)) =C ^((k)) +P ^((k)) W ^((j)),

where for each k, either a 0 or a 1 is assigned to j. It should again beemphasized that the above is only an example of the waveform modulationprocess of the invention. As previously noted, alternative embodimentscould utilize other modulation techniques.

FIG. 4 shows a block diagram of a coherent detector 40 for detecting adigital image watermark of the type inserted by the encoder 30 of FIG.3. A given channel bit of the inserted watermark is detected bycorrelating an n-bit extracted sequence s against both s^((k),0) ands^((k),1) in a correlator 44. The extracted sequence may be generated bysubtracting the known unwatermarked image data for that sequence fromthe corresponding watermarked image data in element 42. Alternatively,the element 42 may be eliminated and the watermarked image data applieddirectly to the correlator 44. The correlator 44 makes a decision as tothe value of the corresponding bit of the digital watermark based onwhich correlation is highest. This arrangement corresponds generally tothe optimal coherent detector for a known signal observed inindependent, identically-distributed (i.i.d.) Gaussian noise, asdescribed in, e.g., H. V. Poor, “An Introduction to Signal Detection andEstimation,” Springer-Verlag, 1994.

The above-described digital image watermarking process is robust toattack because the potential jammer does not possess exact knowledge ofthe specific channel modulation waveforms used. Although for a randomchoice of waveforms there is a non-zero probability that both will lieclose to each other, resulting in a device with high probability of biterror, this is unlikely to happen. By a straightforward application ofthe well-known Strong Law of Large Numbers (SLLN), one can show that,for large n, ∥s⁰−s¹μ² ≈{square root over (2n)}. Hence, if n is largeenough, one can conclude that with high probability the distanceseparating the modulation waveforms will be large.

Numerical simulations have been performed to illustrate the performanceadvantages of the above-described digital image watermarking techniques.The simulations were performed using a well-known standard test imagereferred to as “Lena.” The 512×512 pixel test image was separated into atotal of 4096 8×8 pixel discrete cosine transform (DCT) blocks. Thenumber of digital watermark information bits B to be stored in the testimage was selected as 32. If B=32 bits can be stored in the imagereliably, then 2³²≈4·10⁹ distinct watermarks can be distinguishedreliably, a number useful for many practical applications. These 32digital watermark information bits were mapped to 4096 channel bitsusing a simple (128,1,128) replication code.

In order to measure the robustness of the digital watermarkingtechniques, the probability of watermark decoding error was estimatedfor different noise variances. The estimates were made by first taking arandom sequence of 32 bits, storing them in the image, adding noise tothe image, and retrieving the stored bits. This process was thenrepeated 1000 times, and the probability of error estimated as the ratioof the number of incorrectly decoded watermarks to 1000. Also, in orderto measure how image quality degrades as a function of jammer noise, thepeak signal-to-noise ratio (PSNR) of the noisy image is computed againstthe clean original, for a number of different noise variance values. ThePSNR for images assumes a peak pixel intensity value of 255. FIG. 5shows the resulting plot of the estimated probability of error, and FIG.6 shows the resulting plot of the PSNR, both as a function of σ.

It can be seen from the plots of FIGS. 5 and 6 that for values of a upto about 3.5, the number of incorrectly retrieved watermarks over 1000tests is zero, and that for a value of σ=3.5, a typical corrupted imageachieves a PSNR value of only about 28.8 dB. Moreover, using thecapacity formula given previously, with σ=3.5, C(σ)=9970 bits, which issignificantly more than the 32 bits stored in the example.

A more complex modulation process could be used in order to increase thenumber of distinct watermarks that can be generated. For example, higherrate codes could be used to increase the number of bits that can bereliably stored in the array, at the expense of added computationalcomplexity.

It should be noted that the above-described additive noise model may notprovide suitable approximations for certain types of distortions. Forexample, the additive noise model is generally not a good model forgeometric distortions.

It should also be noted that a frame-by-frame application of theabove-described techniques to video generally yields poor performance.However, the techniques of the invention can be used in conjunction withother types of storage array models in order to improve performance forvideo or other types of electronic data.

The above-described embodiments of the invention are intended to beillustrative only. For example, although illustrated using coherentdetection, the invention can also be implemented using other types ofdetection arrangements, including non-coherent detection. Moreover, theparticular encoding and decoding architectures shown are examples only,and other types of encoding and decoding devices may be used toimplement the watermarking techniques of the invention. These andnumerous other embodiments within the scope of the following claims willbe apparent to those skilled in the art.

What is claimed is:
 1. A method for inserting digital watermarkinformation into an image, the method comprising the steps of:separating the image into a plurality of components; and associating oneor more bits of the digital watermark information with each of at leasta subset of the plurality of components of the image, by modulating eachof the components in the at least a subset of the plurality ofcomponents with a corresponding modulation waveform representative of atleast a portion of the one or more bits.
 2. The method of claim 1wherein the separating step includes separating the image into aplurality of discrete cosine transform (DCT) blocks of a predetermineddimension.
 3. The method of claim 1 wherein the separating step includesseparating the image into a plurality of image subband components. 4.The method of claim 1 wherein the digital watermark information includesa total of B bits of information for representing a particularwatermark, such that M=2^(B) distinct watermarks can be generated usingthe B information bits.
 5. The method of claim 4 further including thestep of mapping the B information bits to N channel bits using an (M, N)code, where M=2^(B) is the number of distinct watermarks, and Ncorresponds to the block length of the code and the number of imagecomponents generated in the separating step, and wherein the associatingstep includes associating a given one of the N channel bits with acorresponding one of the N image components.
 6. The method of claim 1wherein the modulation waveform comprises a selected one of a set oforthogonal modulation waveforms.
 7. The method of claim 1 wherein themodulation waveform comprises a selected one of a pair of vectorss^((k),b)=[s^((k),b) . . . s^((k),b)] having a zero mean and an identitycovariance matrix.
 8. The method of claim 7 wherein b has a value oflogic zero or logic one, such that s^((k),0) is representative of a bitof digital image watermark information having a value of logic zero, ands^((k),1) is representative of a bit of digital image watermarkinformation having a value of logic one.
 9. The method of claim 1further including the step of applying a visual model to determine atleast one of: (i) which of the plurality of image components are to beassociated with one or more bits of the digital watermark information,and (ii) the manner in which the modulation waveform is applied to agiven one of the image components.
 10. The method of claim 1 wherein anupper bound on the total number of bits in the digital watermarkinformation is given by:${\frac{nN}{2}{\log \left( {1 + \frac{1}{\sigma^{2}}} \right)}},$

where N corresponds to the number of image components generated in theseparating step, n is the number of bits of the digital image watermarkinformation associated with each of the N components, and σ² is ameasure of noise variance associated with a potential jammer of theinformation.
 11. An apparatus for inserting digital watermarkinformation into an image, the apparatus comprising: an encoderoperative to associate one or more bits of digital watermark informationwith each of at least a subset of a plurality of components of theimage, by modulating each of the components in the at least a subset ofthe plurality of components with a corresponding modulation waveformrepresentative of at least a portion of the one or more bits.
 12. Theapparatus of claim 11 wherein the encoder is further operative toseparate the image into a plurality of discrete cosine transform (DCT)blocks of a predetermined dimension.
 13. The apparatus of claim 11wherein the encoder is further operative to separate the image into aplurality of image subband components.
 14. The apparatus of claim 11wherein the digital watermark information includes a total of B bits ofinformation for representing a particular watermark, such that M=2^(B)distinct watermarks can be generated using the B information bits. 15.The apparatus of claim 14 wherein the encoder is further operative tomap the B information bits to N channel bits using an (M, N) code, whereM=2^(B) is the number of distinct watermarks, and N corresponds to theblock length of the code and the number of image components generated bythe encoder, and wherein the encoder associates a given one of the Nchannel bits with a corresponding one of the N image components.
 16. Theapparatus of claim 11 wherein the modulation waveform comprises aselected one of a set of orthogonal modulation waveforms.
 17. Theapparatus of claim 11 wherein the modulation waveform comprises aselected one of a pair of vectors s^((k),b)=[s₁ ^((k),b) . . . s_(n)^((k),b)] having a zero mean and an identity covariance matrix.
 18. Theapparatus of claim 17 wherein b has a value of logic zero or logic one,such that s^((k),0) is representative of a bit of digital imagewatermark information having a value of logic zero, and s^((k),1) isrepresentative of a bit of digital image watermark information having avalue of logic one.
 19. The apparatus of claim 11 wherein the encoder isfurther operative to apply a visual model to determine at least one of:(i) which of the plurality of image components are to be associated withone or more bits of the digital watermark information, and (ii) themanner in which the modulation waveform is applied to a given one of theimage components.
 20. The apparatus of claim 11 wherein an upper boundon the total number of bits in the digital watermark information isgiven by:${\frac{nN}{2}{\log \left( {1 + \frac{1}{\sigma^{2}}} \right)}},$

where N corresponds to the number of image components, n is the numberof bits of the digital image watermark information associated with eachof the N components, and σ² is a measure of noise variance associatedwith a potential jammer of the information.
 21. An article ofmanufacture comprising a machine-readable storage medium containing oneor more software programs which when executed implement the steps of:separating the image into a plurality of components; and associating oneor more bits of the digital watermark information with each of at leasta subset of the plurality of components of the image, by modulating eachof the components in the at least a subset of the plurality ofcomponents with a corresponding modulation waveform representative of atleast a portion of the one or more bits.
 22. An apparatus for detectingdigital watermark information inserted into an image, the apparatuscomprising: a decoder operative to generate an estimate of one or morebits of digital watermark information for each of at least a subset of aplurality of components of the image, wherein each of the components inthe at least a subset of the plurality of components are modulated witha corresponding modulation waveform representative of at least a portionof the one or more bits.